I'd like to solve the below highly nonlinear ODEs with constraint equations. Eq 1 is a 2nd order ODE, so I need two BCs where only one BC is specified and the other should be determined by Eq2. I have no clue on how to approach this kind of problem and don't know how to use Eq 2. I really appreciate that if you could give me some helps to resolve those constraints in terms of numerics. Thanks.